From 4780106a4f191c41d3b82ca9d1327a1c95a72055 Mon Sep 17 00:00:00 2001 From: Prefetch Date: Thu, 27 May 2021 20:46:01 +0200 Subject: Expand knowledge base --- content/know/concept/superdense-coding/index.pdc | 33 +++++++++++++++++++----- 1 file changed, 27 insertions(+), 6 deletions(-) (limited to 'content/know/concept/superdense-coding') diff --git a/content/know/concept/superdense-coding/index.pdc b/content/know/concept/superdense-coding/index.pdc index e50be2b..1a9337c 100644 --- a/content/know/concept/superdense-coding/index.pdc +++ b/content/know/concept/superdense-coding/index.pdc @@ -32,12 +32,33 @@ Based on the values of the two classical bits $(a_1, a_2)$, Alice performs the following operations on her side $A$ of the Bell state: -| $(a_1, a_2)$ | Operator $\qquad$ | Result | -|:--:|:--|:---------| -| $00$ | $\hat{I}$ | $\ket*{\Phi^{+}} = \frac{1}{\sqrt{2}} \Big(\ket{0}_A \ket{0}_B + \ket{1}_A \ket{1}_B \Big)$ | -| $01$ | $\hat{\sigma}_z$ | $\ket*{\Phi^{-}} = \frac{1}{\sqrt{2}} \Big(\ket{0}_A \ket{0}_B - \ket{1}_A \ket{1}_B \Big)$ | -| $10$ | $\hat{\sigma}_x$ | $\ket*{\Psi^{+}} = \frac{1}{\sqrt{2}} \Big(\ket{0}_A \ket{1}_B + \ket{1}_A \ket{0}_B \Big)$ | -| $11$ | $\hat{\sigma}_x \hat{\sigma}_z$ | $\ket*{\Psi^{-}} = \frac{1}{\sqrt{2}} \Big(\ket{0}_A \ket{1}_B - \ket{1}_A \ket{0}_B \Big)$ | + + + + + + + + + + + + + + + + + + + + + + + + + + +
$(a_1, a_2)$OperatorResult
$00$$\hat{I}$$\ket*{\Phi^{+}} = \frac{1}{\sqrt{2}} \Big(\ket{0}_A \ket{0}_B + \ket{1}_A \ket{1}_B \Big)$
$01$$\hat{\sigma}_z$$\ket*{\Phi^{-}} = \frac{1}{\sqrt{2}} \Big(\ket{0}_A \ket{0}_B - \ket{1}_A \ket{1}_B \Big)$
$10$$\hat{\sigma}_x$$\ket*{\Psi^{+}} = \frac{1}{\sqrt{2}} \Big(\ket{0}_A \ket{1}_B + \ket{1}_A \ket{0}_B \Big)$
$11$$\hat{\sigma}_x \hat{\sigma}_z$$\ket*{\Psi^{-}} = \frac{1}{\sqrt{2}} \Big(\ket{0}_A \ket{1}_B - \ket{1}_A \ket{0}_B \Big)$
Her actions affect the state on Bob's side $B$ due to entanglement. Alice then sends her qubit $A$ to Bob over the quantum channel, -- cgit v1.2.3